小学数学找规律题

一：

1/2*3 = 1/2 - 1/3
1/3*4 = 1/3 - 1/4
...
1/99*100 = 1/99 - 1/100

所以：
1/2*3+1/3*4+1/4*5+1/5*6*1/6*7+。。。。。+1/99*100
＝(1/2 - 1/3 + 1/3 - 1/4 +...+1/99 - 1/100)
＝(1/2 - 1/100)
＝49/100

二：
1/3 = 1/1*3 = (1/1 - 1/3)/2
1/15 = 1/3*5 = (1/3 - 1/5)/2
1/35 = 1/5*7 = (1/5 - 1/7)/2
...
1/143 = 1/11*13 = (1/11 - 1/13)/2

1/3+1/15+1/35+1/63+1/99+1/143
= (1/1 - 1/3 + 1/3 - 1/5 + ... + 1/11 - 1/13)/2
= (1 - 1/13)/2
= 6/13

1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+......+1/99*100

=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+......+(1/99-1/100)

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+......+1/99-1/100

=1/2-1/100

1/3+1/15+1/35+1/63+1/99+1/143

=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11&13

=(1-1/3)* 1/2+(1/3-1/5)* 1/2+(1/5-1/7)* 1/2+......+(1/11-1/13)*1/2

=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+......+1/11-1/13)* 1/2